Question

Find two consecutive even numbers such that the difference of one-half the larger number and two-fifths the smaller number is equal to five.
38 and 40
40 and 42
42 and 44

Answer 1

40 and 42..................

Answer 2

Answer:

The correct option is 2. The consecutive even numbers are 40 and 42.

Step-by-step explanation:

Let the two consecutive even numbers be x and x+2.

It is given that the difference of one-half the larger number and two-fifths the smaller number is equal to five.

$\frac{1}{2}(x+2)-\frac{2}{5}(x)=5$

$\frac{x+2}{2}-\frac{2x}{5}=5$

$\frac{5x+10-4x}{10}=5$

$x+10=50$

$x=50-10$

$x=40$

The value of x is 40. Therefore the two consecutive even numbers are 40 and 42.

Option 2 is correct.